Automated or data-driven bandwidth selection methods tend to break down in the presence of correlated errors. While this problem has been previously studied in the context of fixed design for kernel regression, the results have only been applicable when some prior knowledge or parametric form of the correlation structure is available or assumed. In this presentation we generalize these results to the random design setting and address the problem when no prior knowledge or any parametric structure is available about the correlation function. In this talk we show that, under mild conditions, the local polynomial regression estimator is consistent under the assumed model structure . Also, we show the asymptotic optimality of our proposed bandwidth selection criterion based on a special family of kernels. This work is authored with Irène Gijbels (KU Leuven, Belgium) and Jean Opsomer (CSU, Fort Collins).